THATCHER, GORBACHEV CAN `DO BUSINESS' DESPITE DIFFERENCES

He heads the world's foremost Marxist government; she firmly believes that "Marxism's had it."

Despite their political differences, however, Soviet leader Mikhail S. Gorbachev and British Prime Minister Margaret Thatcher seem to get along famously. They are scheduled to meet again April 5-7, when Gorbachev visits Britain.The rapport between the two leaders dates from their first encounter five years ago. In a comment widely quoted afterward, Thatcher said: "I like Mr. Gorbachev - we can do business together."

Gorbachev returned the favor by treating Thatcher with unusual consideration during her visit to the Soviet Union in March 1987. The two conferred for about 12 hours in all, and the visit ended with a 50-minute Thatcher news conference that was shown in its entirety on Soviet television. Parrying hostile questions with aplomb, the prime minister left some of the Soviet journalists visibly nonplused.

Thatcher's performance in Moscow earned her plaudits in the British press, and she lost little time in turning the praise to political advantage. Six weeks after her return, she called for general parliamentary elections. The conservative Party was returned to power with a 101-seat majority, making Thatcher the first British head of government in 160 years to be elected to three consecutive terms.

In power for nearly a decade now, Thatcher is the senior national leader of the Western alliance. As such, she commands an extra measure of respect both within the alliance and in other world councils. During the Reagan administration, she acted as an interlocutor, helping to keep lines of communication open between Moscow and Washington.

Some commentators have suggested that Thatcher's Britain could serve as a role model for the Soviet Union as it adjusts to Gorbachev's perestroika policies. When Thatcher first took office in 1979, Britain lagged well behind other Western European nations in productivity and output. Today, it is among the growth leaders.

One issue that is sure to figure prominently in the coming Gorbachev-Thatcher talks is the Western economic sanctions imposed on the Soviet Union after its forces invaded Afghanistan in late 1979.

Whatever the outcome of that debate, it is safe to say that blunt language as well as mutual respect will mark the talks between Gorbachev and Thatcher. Both are renowned for their love of a good argument. Both are also known for being wary of one another.